The historical context of Arf's
work on quadratic forms in characteristic 2, including a biography,
his correspondance with his thesis adviser Helmut Hasse and an
appendix correcting in error in the 1941 paper.

Early work on
the stable 2-stem.Thanks to Andrew Ranicki for finding
these.

Solution to an analogous problem
at primes larger than 3. The methods used there to detect the
elements in question (Theorem 6.4.4) were similar in spirit to our
proof of the Detection
Theorem. The problem at the prime 3 remains open.

This paper studies MU as
a C2-equivariant spectrum. Their Proposition 4.9
is our Reduction Theorem (in Section 7
of our preprint) for the
group C2. They also prove a special case of our
Slice Differentials Theorem (10.9).

We now know that the only
dimensions in which there are framed manifolds with Kervaire invariant
one are 2, 6, 14, 30, 62 and possibly 126.
"The hunt to find examples in these six special cases has
begun!"

"In
the 1965
Hedrick Lectures, I described the state of Differential Topology,
a field which was then young but growing very rapidly.
....
The question as to just when Φk = 0 was the last major
unsolved problem in understanding the group of homotopy spheres. It
has recently been solved in all but one case by Hill, Hopkins, and
Ravenel."

Writeup of a course given in
Barcelona in 2010. It includes a proof (in Remark 2.7) that the category of
orthogonal equivariant G-spectra, defined by Mandell-May and
used by us, is equivalent to the category of orthogonal spectra
with G-action.

"Hill, Hopkins, and Ravenel
(hereafter HHR) marshall three major developments in stable homotopy
theory in their attack on the Kervaire invariant problem:"

The
chromatic perspective based on work of Novikov and Quillen and
pioneered by Landweber, Morava, Miller, Ravenel, Wilson, and many more
recent workers;

The theory of structured ring spectra, implemented
by May and many others; and

Equivariant stable homotopy theory, as
developed by May and collaborators.

"The specific application of
equivariant stable homotopy theory was inspired by analogy with a
fourth development, the motivic theory initiated by Voevodsky and
Morel, and uses as a starting point the theory of 'Real bordism'
investigated by Landweber, Araki, Hu and Kriz. In their application of
these ideas, HHR require significant extensions of the existing state
of knowledge of this subject, and their paper provides an excellent
account of the relevant parts of equivariant stable homotopy theory."

We present an introduction to
the equivariant slice filtration. After reviewing the definitions
and basic properties, we determine the slice dimension of various
families of naturally arising spectra. This leads to an analysis of
pullbacks of slices defined on quotient groups, producing new
collections of slices. Building on this, we determine the slice
tower for the Eilenberg-Mac Lane spectrum associated to a Mackey
functor for a cyclic p-group. We then relate the Postnikov tower
to the slice tower for various spectra. Finally, we pose a few
conjectures about the nature of slices and pullbacks.